Comparison
of IBFV, LEA, UFAC, and AUFLIC
/ UFLIC
in temporal-spatial coherence(click for the
animations)

IBFV [1],
LEA [2], UFAC [3],
and AUFLIC / UFLIC [4]
are the most competitive methods for visualizing unsteady flow fields, each
with its own advantages and disadvantages. Each IBFV frame is the result
of Line Integral Convolution [5]
of a sequence of images along pathlines. The exponential decay convolution
filter used in IBFV to low-pass filter noise textures is well suited for
introducing temporal coherence in the animation, however, the spatial coherence
it constructs in each frame may be insufficient. Thus flow directions are
either noisy or artificially blurred [3]
as the texture-scale varies (Figure
1). Second,
the increasing (unsteady) flow complexity greatly compromises the performance
unless the field is highly sub-sampled to create a warping mesh, as was
done in [1], [6]
in order to achieve high frame rates. Third, 3D IBFV is limited in the range
of velocities it can display as stated in [7].
Fourth, 3D IBFV handles only time-independent 3D flows since time-varying
flows require a continuous update of the velocity texture [7],
which is difficult to achieve. Finally, IBFV depends on hardware capabilities
coupled with single-step forward integration to achieve high frame rates.

(a)
A smaller texture scale is used (169k).

(b)
A larger texture scale is used (171k).

Figure
1. IBFV images produced by Jarke J. van Wijk (http://www.win.tue.nl/~vanwijk/ibfv/,
posted on Dec 22, 2003). The flow directions are either noisy in (a)
or blurred in (b) as the texture scale varies.

LEA
also employs single-step integration, though backward, to access the last
frame for advected texture values. It resorts to blending of successive
textures to represent spatial correlation along a dense set of pathline
segments to approximate short streamlines, but the exponentially decreasing
temporal filter does not produce sufficient spatial coherence either [3].
Despite the application of LIC to suppress aliasing artifacts created where
the noise is advected more than one cell per integration, only shorter kernel
lengths can be used since streamlines would otherwise significantly deviate
from actual pathlines, causing flashing in the animation and degraded image
contrast. Thus there exists a trade off between the spatial coherence in
an image and the temporal coherence in the animation. Flow directions are
noisy / obscure in low-magnitude areas when the length of the streaks is
proportional to the velocity magnitude (Figure
2).

Figure
2. An LEA image (with velocity masking) produced by Bruno Jobard et
al. (http://www.cscs.ch/~bjobard/Research/
Publications/vis2001/gulf_of_mexico_images.htm, posted
on Dec 22, 2003). The flow directions in high-magnitude areas are
clear while the flow directions in low-magnitude areas are very obscure
as the length of streaks is proportional to the flow velocity magnitude.
When the velocity mask is turned off or the masking parameter is tuned,
the "hiden" noisy pattern will emerge as it is (9.75M).

UFAC
was derived from a generic spacetime-coherent framework, which provides
an explicit, direct, and separate control over temporal coherence and spatial
coherence to emulate IBFV, LEA, and UFLIC. However, as stated in [3],
it still fails to solve the inconsistency between temporal and spatial patterns
since the evolution of streamlines along pathlines might not lead to streamlines
of the subsequent time step. Its ad hoc solution to this problem is limited
to only an explicit control over the length of the spatial structures based
on the flow unsteadiness to retain temporal coherence. In regions where
the flow changes rapidly, the correlated segments along streamlines have
to be very short and even degenerate to points (particles) to suppress flickering,
which inevitably affects spatial coherence. As a result, high spatial coherence
in a frame causes flickering artifacts in the animation while high temporal
coherence in the animation causes a noisy pateern in the constitunent frames.
In a word, UFAC can not achieve both high temporal coherence and high spatial
coherence, i.e., one is achieved at the cost of the other (Figure
3). Finally,
UFAC is limited to DirectX 9.0 compliant GPUs, or OpenGL with fragment support
(pixel shader programs).

(a)
UFAC-emulated LEA (927k).

(b)
UFAC without velocity masking (983k).

(c)
Application of long-kernel LIC filtering (983k).

Figure3.
UFAC images produced by Daniel Weiskopf et al. (http://www.vis.uni-stuttgart.de/ufac/ufac/,
posted on April 27, 2004). UFAC-emulated LEA achieves good temporal
coherence, but very poor spatial coherence (a very noise pattern)
in (a). Temporal coherence degrades (notice the flickering artifacts
in the movie) as spatial coherence improves a little (still noisy
in regions where the flow changes rapidly) in (b). Temporal coherence
becomes very poor (notice the severe flickering artifacts in the movie)
except for regions of small unsteadiness when long-kernel LIC filtering
is applied to show clear long streamlines in (c).

AUFLIC
/ UFLIC possesses the advantage of conveying very high temporal and spatial
coherence by scattering fed-forward texture values. Value scattering along
a long pathline over several time steps not only correlates a considerable
number of intra-frame pixels to establish strong spatial coherence, but
also correlates sufficient inter-frame pixels to build tight temporal coherence.
Texture feed-forwarding that takes an output frame, after noise-jittered
high-pass filtering, as the input texture for the next frame constructs
an even closer correlation between the two consecutive frames to enhance
temporal coherence. Flow directions are clearly depicted in individual images
for instantaneous flow investigation and the animation is also quite smooth
(Figure
4). The
inconsistency between temporal and spatial patterns in IBFV, LEA, and UFAC
is successfully resolved by scattering fed-forward texture values in AUFLIC
/ UFLIC. Also, AUFLIC / UFLIC can be easily extended to time-varying 3D
flows [8], [9].

(a)
Vortex data set (17.00M).

(b)
Weather data set (6.94M).

Figure
4. AUFLIC images produced by Zhanping Liu and Robert J. Moorhead II.
Note the flow directions are very clear (neither noisy nor blurred)
thanks to strong spatial coherence. The resulting animations are very
smooth (without artifacts or flickering) due to high temporal coherence.